A093121 A Jacobsthal Fibonacci product.

1, 0, 4, 6, 30, 80, 286, 882, 2924, 9350, 30438, 98208, 318278, 1029210, 3331820, 10780014, 34888062, 112894960, 365344142, 1182264930, 3825911596, 12380874550, 40065409014, 129654294336, 419570260150, 1357757640330

Offset

0,3

Comments

Form a graph from a triangle and its midpoint triangle. A093121 counts closed walks of length n at a vertex of the midpoint triangle in this configuration.

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (1,7,2,-4).

Formula

G.f.: (1-x-3x^2)/((1+x-x^2)(1-2x-4x^2));

a(n)=A078008(n)*A000045(n+1);

a(n)=(2^n/3+2(-1)^n/3)(((1+sqrt(5))/2)^(n+1)/sqrt(5)-((1-sqrt(5))/2)^(n+1)/sqrt(5)).

Mathematica

LinearRecurrence[{1, 7, 2, -4}, {1, 0, 4, 6}, 30] (* Harvey P. Dale, Aug 26 2019 *)

Crossrefs

Sequence in context: A090530 A154667 A376482 * A248048 A209298 A075590

Adjacent sequences: A093118 A093119 A093120 * A093122 A093123 A093124

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2004

Status

approved